TORONTO/NEW YORK (Reuters) - Milestone Apartments Real Estate Investment Trust, which has agreed to be acquired by Starwood Capital Group for about C$1.7 billion ($1.3 billion), is in talks with the U.S. private investment firm about raising its bid, people familiar with the situation told Reuters.

Milestone’s units MST_u.TO, which were unchanged before the Reuters report, rose as much as 2.7 percent to a one-month high of C$21.62, as volume jumped, crossing the current offer value of C$21.18. They closed up 2 percent at C$21.49 on Monday.

Both the broader Toronto composite stock market .GSPTSE and the Canadian REIT sector index .GSPRTRE ended in the red on Monday.

Milestone and Starwood could agree on a higher price and make an announcement early this week, the sources said on Monday. But they cautioned there was no certainty a deal would be reached at a higher price.

The sources declined to be identified as the talks are confidential. Representatives of both Milestone and Starwood declined to comment.

On Jan. 19, Milestone agreed to be bought out by Starwood for $16.15 per Milestone unit in an all-cash transaction.

Based on currency exchange rates at the time, it translated to a premium of about 9.2 percent above the units’ closing price of C$19.66 before the transaction was announced.

Manash Goswami, portfolio manager at First Asset Investment Management Inc, said he was unhappy with the current offer.

“We would like to see a bid north of $17. At $17, it is about (a) 10 percent premium to consensus net asset values out there,” Goswami said. First Asset owns Milestone units.

Dallas-based Milestone, which went public in Toronto in 2013, owns and manages apartment properties targeting blue-collar workers across the U.S. Southeast and Southwest.

With a focus on real estate, Barry Sternlicht-led Starwood Capital manages assets of about $52 billion.

Last week, proxy advisory service Glass Lewis encouraged unitholders to vote for the transaction, while ISS went the other way.

“The fact pattern in the transaction indicates speed and certainty were prioritized over price, apparently out of concerns that cyclical factors will put pressure on REIT valuations,” ISS said in its report on Feb. 22.

In a response the same day, Milestone said its “board and special committee engaged in a comprehensive process to maximize value for the REIT’s unitholders.”

The trust received some approaches in the past two years, Milestone said in a recent regulatory filing, but had not received an alternative bid since the Starwood deal.

In its report, Glass Lewis said “the purchase price represents a compelling value at which Milestone unitholders can cash out their investment in the REIT and immediately realize an assured value, in cash, at a meaningful premium.”

The deadline to vote on the existing bid is March 3.

($1 = 1.3095 Canadian dollars)

Reporting by John Tilak and Fergal Smith in Toronto, and Carl O'Donnell in New York; Editing by Jeffrey Benkoe and Matthew Lewis